Sudoku XV – Hard

Sudoku XV

Sudoku XV is a variant of classic Sudoku with additional markings between neighboring cells. A V means that the two adjacent numbers add up to 5. An X means they sum to 10.

The regular Sudoku rules remain fully in effect. The X and V markings provide additional local sum hints. In the fully marked form, it also states: If no X or V stands between two neighboring cells, these two numbers do not sum to 5 or 10.

Basic Rules

• Each row must contain the numbers 1 to 9 exactly once.
• Each column must contain the numbers 1 to 9 exactly once.
• Each 3x3 block must contain the numbers 1 to 9 exactly once.
• A V between two neighboring cells means: The two numbers sum to 5.
• An X between two neighboring cells means: The two numbers sum to 10.
• The markings only apply to directly neighboring cells, horizontally or vertically.
• In fully marked XV puzzles, a missing marking indicates the two numbers do not sum to 5 or 10.

Strategies for Solving

XV hints provide fixed number pairs. For V, only the pairs 1+4 and 2+3 are possible. For X, several pairs are possible: 1+9, 2+8, 3+7, and 4+6.

1. Immediately Narrow V-Pairs

A V hint reduces two cells to a few possibilities. In the following example, in the first row, there's a V between 4 and the empty cell.

The two numbers must sum to 5, so the empty cell must be 1.

The V marking here provides a direct, safe entry.

2. Combine X-Pairs with Sudoku Rules

An X hint means sum 10. If one number is known, the other is immediately determined.

Here, a 1 must go in the empty cell next to the 9, since only 1 + 9 makes 10.

Afterward, the 1 can be eliminated from the rest of the row, column, and associated 3x3 block.

3. Use Missing Markings as Exclusions

In fully marked XV puzzles, the absence of a marking is also informative.

In this example, no 4 or 9 can go into the three cells to the right, above, and below the 1. These numbers would sum to 5 or 10 and would require a V or X in between. Since no marking exists, 4 and 9 are excluded.

This step does not assign a number yet but removes important candidates.

Typical Solving Sequence

1. Check all V hints first because they allow only a few pairs.
2. Then examine X hints with known neighboring numbers.
3. List possible pairs for each marked neighbor pair.
4. Use missing markings as exclusions if the puzzle is fully marked.
5. Combine XV pairs with rows, columns, and blocks.
6. Update candidates after each new entry.

Common Mistakes

• Confusing V and X: V means 5, X means 10.
• Solving a marked pair in isolation and forgetting Sudoku rules.
• Not using missing markings as exclusions in fully marked puzzles.

Tips for Beginners

• Remember V pairs 1+4 and 2+3.
• Remember X pairs 1+9, 2+8, 3+7, and 4+6.
• If one number of a marked pair is known, immediately determine the other.
• Use XV hints mainly for candidate elimination.
• After each pair, check if a new single candidate appears in the row or block.

Sudoku XV is very accessible because the additional rule is simple. Nonetheless, many strong deductions arise when analyzing marked and unmarked neighbor pairs systematically.